Production of Ionizing Radiation - Lecture Notes

Learning Objectives

Understand common medical uses for ionizing radiation.
Explain the benefits and drawbacks of different types of radiotherapy methods.
Understand what is meant by ionizing radiation.
Identify typical wavelengths/photon energies for X-rays and other photons.
Understand the circumstances under which unstable nuclei give rise to α, β, and γ decays, and be able to describe the decay products.
Be able to determine the number of radioactive nuclei or activity as a function of time, using the half-life.

Biomedical Applications of Ionising Radiation (Nuclear Medicine)

Medical Imaging
- Common forms of imaging: X-rays, computed tomography, positron emission tomography
Radiation therapy (radiotherapy)
- Typically for cancer treatment
Sterilization of medical devices
- Typically gamma rays
- Often used for items that are completely sealed, e.g., surgical gloves, sutures

Radiation Therapy

Tumor cells are more sensitive to radiation damage than normal cells.
Ionizing radiation is used to damage the DNA of cancerous cells.
The right type, energy, and dose of the radiation are important.
The radiation must be shaped so that it is focused on the tumor to prevent damage to the tissue it needs to pass through.
There is often skin damage over multiple sessions.

Radiation Therapy Methods

Radiation types
- X-rays from X-ray tubes
- X-rays and electrons from linear accelerators
- Gamma rays from internal or external sources
- Proton beams

Linear Accelerator

High energy X-rays: 4 - 25 MeV
For comparison, diagnostic x-rays are in the 20-160keV range.
Different accelerating method than in the X-ray tube.
Uses a type of particle accelerator and electric fields to speed up particles.

Tele-isotope Unit

𝛾 source
- $^{60}Co$ source ( $T_{1/2}$ = 5.26 years, 1.17 MeV and 1.33MeV)
- $^{137}Cs$ source ( $T_{1/2}$ = 30 years, 0.66 MeV)
Not as common
Cannot be turned off
Typically more reliable, simple to maintain
Low power

Radiotherapy Video Example

Example video demonstrating radiotherapy techniques.

Radiation Therapy Side Effects

Radiation dermatitis (Grades 2 and 3) can occur as a side effect.

Brachytherapy

Sealed radiation source implanted.
Localized irradiation, minimizes side effects to surrounding tissue.
Good if there is movement of tumor or movement of patient during therapy.
Minimize clinic visits
Common for prostate cancers.

Hadron (Proton) Therapy

Comparison of dose distribution between photons and protons.
Bragg peak: A pronounced peak on the Bragg curve which plots the energy loss of ionizing radiation during its travel through matter. For protons, α-rays, and other ion rays, the peak occurs immediately before the particles come to rest.

Microbeam Radiation Therapy

Research into this new technique that requires very bright radiation but lower dose.
The beamlets are 100-300 microns apart (100 microns is roughly the width of a human hair) and each beamlet is 10-50 microns wide.

Gamma Knife

201 Co-60 sources of ~1mm diameter each held in a collimator 'helmet'.

Total Body Irradiation

Radiation is delivered to the whole body.
Typically done before a stem cell or bone marrow transplantation.
Done to suppress the body’s immune response to help prevent rejection of donor cells.
Can also be used to kill any remaining cancerous cells.

Total Body Irradiation Methods

Radiation delivered over multiple sessions (also done for radiation therapy).
Dose fractionation is when the dose of radiation is split over multiple sessions/days.
- E.g., doses given once a week over multiple weeks.
- This is done to minimize side effects and allow non-cancerous cells time to recover.

Total Body Irradiation Methods: Fractionation of Radiation Doses

Hypofractionation: higher doses, fewer sessions. Used for aggressive tumor growths.
Hyperfractionation: lower doses, more sessions.
Accelerated fractionation: lower doses, more sessions but delivered in a shorter amount of time (e.g., often multiple sessions per day): Used to stop tumor cell regeneration between treatments.

What is Ionising Radiation?

A particle (wave) that has sufficient energy to ionize atoms
Usually produced one of two ways:
1. Acceleration of charged particles
 - X-rays – high energy photons (0.1-100 keV)
2. Radioactive (nucleus) decay
 - α (alpha) radiation: $^4_2He^{2+}$
 - β or β- (beta) radiation: $^01e$ ( $e^+$ $, positron) or $^0{-1}e$ ( $e^-$ $, electron)
 - 𝛾 (gamma) radiation: very high energy (1-100 MeV) photons
 - n (neutrons)
 - p (protons)

What is a Photon?

A quantum of energy: $E_{photon} = hf = \frac{hc}{\lambda}$
- Planck’s constant: $h = 6.626 \times 10^{-34} Js$
- Frequency [Hz, s-1]: $f$
- Wavelength [m]: $\lambda$
- Speed of light [m/s]: $c = \lambda f$

Electromagnetic (EM) Waves = Photons

In vacuum: $c = f\lambda$ , where c is the speed of light, f is the frequency, and $\lambda$ is the wavelength.

E-M Spectrum

Illustrates the electromagnetic spectrum, ranging from radio waves to gamma rays, highlighting the positions of microwave, infrared, visible light, ultraviolet, and X-rays.
Indicates the frequency, energy, and wavelength associated with each type of radiation, and specifies which types are ionizing.

Electron-Volt

Unit of energy
Defined as the energy required to accelerate an electron through a potential of 1V
$1eV = 1.6 \times 10^{-19}J$
$E{keV} = \frac{12.4}{\lambda{\text{\AA}}}$ where 1Å = 10^{-10} m [NOT an SI unit!]

Radioactivity

Many naturally occurring nuclei are unstable, giving rise to radioactive isotopes.
Some radioactive isotopes are naturally produced, e.g., cosmic radiation.
It is also possible to artificially produce many radioactive isotopes.
Radioactive elements (or their decay products) are used for imaging (e.g., PET) and radiotherapy (e.g., brachytherapy)
Example: 99mTc labelled metastases, 𝛾 = 140keV

Radioactivity Nobel Prize

Henri Becquerel, Marie and Pierre Curie
- 1896 — radioactivity
- 1898 — Polonium and Radium

Atom

1 fm = 10-15 m
1 Å = 10-10 m
Proton size: 0.84 - 0.87 fm
Neutron size: 0.3 - 2 fm
Nucleus radius ~ 10 fm
Atom’s radius ~ 1 Å
Proton mass: 1.673 x 10-27 kg
Neutron mass: 1.675 x 10-27 kg
Electron mass: 9.1 x10-31 kg

Nuclear Structure – Notation Reminder

(Atomic) Mass number A = Z + N, number of nucleons
Atomic number Z - number of protons, defines element
N - numbers of neutrons
Representation: $^A_ZX$

Nuclear Structure

Isotopes have the same Z (e.g., $^{12}C$ and $^{14}C$ )
Isotones have the same N (e.g., $^{12}B$ and $^{13}C$ , 7 neutrons)
Isobars have the same A (e.g., $^{14}C$ , $^{14}N$ , $^{14}O$ )
Isomers have the same A, Z, N, Atom is in the excited state (e.g. $^{99m}_{43}Tc$ , m stands for metastable state)
Representation: $^A_ZX$

Stable Nuclei

Small number of nuclei are stable.
No stable nuclei with Z>83
Heavy nuclei
More protons than neutrons
More neutrons than protons

α Decay

$^AZX \rightarrow ^{A-4}{Z-2}Y + \alpha$ , where α-particle is $He$

β- Decay (Electron)

$^AZX \rightarrow ^A{Z+1}Y + \beta^- + \bar{\nu}$
$n \rightarrow p^+ + \beta^- + \bar{\nu}$

β+ Decay (Positron)

$^AZX \rightarrow ^A{Z-1}Y + \beta^+ + \nu$
$p^+ \rightarrow n + \beta^+ + \nu$

𝛾 Decay

Excited state of the nucleus decays into ground state, emitting a photon.
$^AZX^* \rightarrow ^AZX + \gamma$

Decay Diagram

Representation of different decay modes (α, β+, β-) on a chart of nuclides.

Radioactive Decay

Radioactive decay is statistical and unpredictable.
Individual atoms have an equal chance of decay – we can only characterise the average rate of decay (disintegration).
The probability of any decay over some time interval dt is proportional to the number N of unstable nuclei present at time t
λ is the decay constant, units s-1
$\frac{dN}{dt} \propto N$
$\frac{dN}{dt} = - \lambda N$
$N(t) = N_0 e^{-\lambda t}$

Activity

The activity, A, is the rate at which a sample of N atoms decays.
The decay constant, λ, is characteristic of each radionuclide.
Since it gives the probability of decay; it does not depend on the age of the atoms!
SI unit: Bequerel - 1 Bq = 1 decay per second
Old unit: Curie, activity of 1g of radium-226 = 1 Ci = 3.7 x 1010 Bq
$A = \lambda N = \lambda N_0 e^{-\lambda t}$

Half-Life

Decay process is random and statistical.
The nuclei don’t vanish; they might change into different nuclei.
Half-life - time in which half of the radioactive nuclei decay
$A = \lambda N = \lambda N_0 e^{-\lambda t}$
$T_{1/2} = \frac{\ln 2}{\lambda}$
$\ln \frac{N}{N_0} = -\lambda t$

Decay Series

Some unstable nuclei undergo multiple decay paths, with multiple daughters possible, before reaching stable nuclei.
Most naturally occurring radioactive nuclei follow such series, e.g., Thorium, Uranium, Polonium

Interactions With Matter

The probability of an interaction occurring depends on the mass and the charge of the incident particle.

Interactions With Matter

Charged particles can cause ionization and excitations of electrons in medium atoms.
Charged particles interact via Coulomb interactions with electrons in the medium.
Heavy particles can undergo mechanical collisions.
Each interaction transfers some energy from the incident particle to the medium.
Many interactions per particle are possible.

Penetrating Power

Mass and charge matter.
Alpha particles are stopped by paper.
Beta particles are stopped by plastic.
Gamma radiation is attenuated by lead.
Neutrons need concrete for shielding.